1. Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients.
- Author
-
Si, Xinhui, Wang, Chao, Shen, Yanan, and Zheng, Liancun
- Subjects
- *
BOUNDARY value problems , *FRACTIONAL differential equations , *HAAR function , *PARTIAL differential equations , *NUMERICAL analysis , *CAPUTO fractional derivatives , *HADAMARD matrices - Abstract
In this paper, Haar wavelet operational matrix(HWOM) is proposed to solve initial-boundary value problems for a class of time-space fractional partial differential equations of Caputo sense with variable coefficients in both time and space (1) ∑ i = 1 n θ i ∂ γ i u ( x , t ) ∂ t γ i = v ( x , t ) ∂ α u ( x , t ) ∂ x α + d ( x , t ) ∂ β u ( x , t ) ∂ x β + q ( x , t ) , 0 < x < 1 , 0 < t ≤ 1 , as an extension of Rehman and Khan's (2013) work. We obtain a matrix L instead of Q α in Rehman and Khan (2013). when dealing with boundary conditions. By utilizing the operational matrix of fractional integration and Hadamard product,we made an improvement of algorithm to deal with time-space coefficients and gave the error analysis of the HWOM for space-time dimensions. Some numerical results are paralleled with exact solutions to show the efficiency and precision of the presented technique. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF